"Working late hours" means staying at work late in order to finish all the things that you have to do:

Dad used to work late hours every day until his heart attack. These days, he's trying to take it easy.

There's a small difference between "working late hours" and "working overtime". When you "work overtime", it often means that you get paid extra for that time. However, when you have to "put in late hours" at work, you're usually not paid any extra. You're working late in order to accomplish more or to catch up.